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Sinking, Fast and Slow: Relative Volatility Versus Correlation Tightening

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Abstract

Having exhausted the descriptive potential of semideviation and other elaborations of partial statistical moments, I now return to beta as a composite statistic combining relative volatility with correlation. The bifurcation of single-sided beta into distinct components measuring changes in volatility and in correlation reveals two very different aspects of market conduct, each with its own implications for investor behavior.

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Notes

  1. 1.

    Galagedera, An Alternative Perspective, Chap. 5, supra note 43, at 13.

  2. 2.

    Id.

  3. 3.

    See sources cited, Chap. 5, supra note 46.

  4. 4.

    See Estrada, Systematic Risk in Emerging Markets, Chap. 5, supra note 36, at 366; Harvey, Liechty, Liechty & Müller, Chap. 6 , supra note 39, at 469 (describing the “us[e] [of] negative semi-variance in place of variance” as a “three moment optimization method[]”).

  5. 5.

    See Lakshman Alles & Louis Murray, Rewards for Downside Risk in Asian Markets, 37 J. Banking & Fin. 2501–2509, 2501 (2013) (“[T]here is evidence that asset returns [in emerging markets] exhibit very high volatility and are not normally distributed”); Estrada, The Cost of Equity of Internet Stocks, Chap. 6, supra note 1, at 240 (emphasizing downside risk as the proper measure for the cost of equity in speculative securities, such as early Internet stocks); Don U.A. Galagedera & Robert D. Brooks, Is Co-Skewness a Better Measure of Risk in the Downside Than Downside Beta?, 17 J. Multinat’l Fin. Mgmt. 214–230, 216 (2007); Campbell R. Harvey, Predictable Risk and Returns in Emerging Markets, 8 Rev. Fin. Stud. 773–816, 779–780 (1995) (rejecting the null hypothesis of normal markets based on measures of skewness and excess kurtosis in 14 of 20 emerging markets and concluding that “returns in … emerging markets depart from the normal distribution”). See generally Bekaert et al., Chap. 4, supra note 14; Babak Eftekhari & Stephen E. Satchell, International Investors’ Exposure to Risk in Emerging Markets, 22 J. Fin. Research 83–106 (1999).

  6. 6.

    See Soonsung Hwang & Christian S. Pedersen, Asymmetrical Risk Measures When Modelling Emerging Markets Equities: Evidence for Regional and Timing Effects, 5 Emerging Mkts. Rev. 109–128 (2004).

  7. 7.

    See, e.g., Eugene F. Fama & Kenneth R. French, Business Cycles and the Behavior of Metals Prices, 43 J. Fin. 1075–1093 (1988).

  8. 8.

    See José María Montero, Gema Fernández-Avilés & María-Carmen García, Estimation of Asymmetrical Stochastic Volatility Models: Application to Daily Average Prices of Energy Products, 78 Int’l Stat. Rev. 330–347, 330–332 (2010). In Bilski v. Kappos, 561 U.S. 593 (2010), the Supreme Court of the United States of the invalidated a patent asserting a claim over a process for hedging against losses in energy commodities. On the economic impact of irreversible investments in energy, see generally Ben S. Bernanke, Irreversibility, Uncertainty, and Cyclical Investment, 97 Q.J. Econ. 85–106 (1983); Robert S. Pindyck, Irreversibility, Uncertainty, and Investment, 29 J. Econ. Lit. 1110–1148 (1991).

  9. 9.

    See Estrada, Systematic Risk in Emerging Markets, Chap. 5, supra note 36, at 374.

  10. 10.

    Id. at 375; accord Estrada, Downside Risk and Capital Asset Pricing, Chap. 5, supra note 42, at 184.

  11. 11.

    Peter Xu & Rich Pettit, No-Arbitrage Conditions and Expected Returns When Assets Have Different β’s in Up and Down Markets, 15 J. Asset Mgmt. 62–71, 69 (2014); see also id. at 67 (justifying this study’s use of the Russell 3000 “because it excludes the smallest and most illiquid names that may skew the results”); cf. Nurjannah, Galagedera & Brooks, Chap. 4, supra note 73, at 274 (conceding that “increasing global investment flows into Indonesia provide a formidable challenge to equity evaluation due to considerable variation in market conditions and movement”). See generally Elroy Dimson, Risk Measurement When Shares Are Subject to Infrequent Trading, 7 J. Fin. Econ. 197–226 (1977); David J. Fowler & C. Harvey Rorke, Risk Measurement When Shares Are Subject to Infrequent Trading: A Comment, 12 J. Fin. Econ. 279–283 (1983).

  12. 12.

    See Don U.A. Galagedera, Economic Significance of Downside Risk in Developed and Emerging Markets, 16 Applied Econ. Letters 1627–1632, 1632 (2009) (concluding that conventional “CAPM beta clearly outperforms downside beta and downside co-skewness” in developed markets); Don U.A. Galagedera, Relationship Between Systematic Risk Measured in the Second-Order and Third-Order Co-Moments in the Downside Framework, 3 Applied Fin. Econ. Letters 147–153, 152 (2007) (concluding that “variation in the difference between systematic risk measures in terms of co-semi-skewness and co-semi-variance is larger in emerging markets than in developed markets”). See generally Harvey, Predictable Risk and Returns in Emerging Markets, supra note 5; Simon Stevenson, Emerging Markets, Downside Risk and the Asset Allocation Decision, 2 Emerging Mkts. Rev. 50–66 (2001).

  13. 13.

    See Tsai, Chen & Yang, Chap. 5, supra note 42, at 447 (finding that downside betas as specified by Hogan & Warren, Chap. 5, supra note 33, and Harlow & Rao, Chap. 5, supra note 37, “outperform[ed]…other betas in explaining the expected stock market returns” in 23 developed countries).

  14. 14.

    See Fletcher, Chap. 4, supra note 66, at 220 (concluding that “there is a conditional relationship between beta and return in UK stock markets” and that “[b]eta seems to be a good indicator of how stocks react in periods of down market months”); David Morelli, Beta, Size, Book-to-Market Equity and Returns: A Study Based on UK Data, 17 J. Multinat’l Fin. Mgmt. 257–272, 265 (2007) (finding “a statistically significant positive relationship” between conditional beta and “realised returns…during up markets and a negative relationship during down markets”); cf. Christian S. Pedersen & Soosung Hwang, Does Downside Beta Matter in Asset Pricing?, 17 Applied Fin. Econ. 961–978, 974 (2007) (concluding that CAPM explains 50–80 % of variations in equity prices, leaving at least 15 % for a lower partial moment version of the CAPM, but ultimately “not … enough to construct a downside risk factor”).

  15. 15.

    See Nikolaos Artavanis, Goerge Diacogiannis & John Mylonakis, The D-CAPM: The Case of Great Britain and France, 2 Int’l J. Econ. & Fin. 25–38, 33 (2010) (concluding that “downside risk measures are better in explaining mean returns” in Great Britain “than the standard deviation and beta,” but only for individual securities and not for portfolios, and concluding from French portfolio results that “downside beta is equivalent or better than the traditional beta in terms of explanatory power when beta and the downside beta are jointly considered”).

  16. 16.

    See Jiro Hodoshima, Xavier Garza-Gómez & Michio Kunimura, Cross-Sectional Regression Analysis of Return and Beta in Japan, 52 J. Econ. & Bus. 515–533, 532 (2000) (concluding that “the conditional relationship” between beta and positive or negative excess returns “is in general better fit in the down market than in the up market”).

  17. 17.

    See Nikolaos G. Theriou, Vassilios P. Aggelidis, Dimitrios I. Maditinos & Želko Sević, Testing the Relation Between Beta and Returns in the Athens Stock Exchange, 36 Managerial Fin. 1043–1056, 1052–1053 (2010).

  18. 18.

    See, e.g., Tim-Alexander Kroencke & Felix Schindler, Downside Risk Optimization in Securitized Real Estate Markets, 28 J. Prop. Inv. & Fin. 434–453 (2010); Kim Hiang Liow, Extreme Returns and Value at Risk in International Securitized Real Estate Markets, 26 J. Prop Inv. & Fin. 418–446 (2008); Tien Foo Sing & Seow Eng Ong, Asset Allocation in a Downside Risk Framework, 6 J. Real Estate Portfolio Mgmt. 213–223 (2000); Petros S. Sivitanides, A Downside-Risk Approach to Real Estate Portfolio Structuring, 4 J. Real Estate Portfolio Mgmt. 159–168 (1998); cf. Camilo Serrano & Martin Hoesli, Are Securitized Real Estate Returns More Predictable Than Stock Returns?, 41 J. Real Estate Fin. & Econ. 170–192 (2010) (suggesting that securitized real estate returns are indeed more predictable).

  19. 19.

    See Henk Grootveld & Winfried Hallerbach, Variance vs. Downside Risk: Is There Really That Much Difference?, 114 Eur. J. Oper. Research 304–319, 315 (1999).

  20. 20.

    See Guido Baltussen, Gerrit T. Post & Pim Van Vliet, Downside Risk Aversion, Fixed Income Exposure, and the Value Premium Puzzle, 36 J. Banking & Fin. 3382–3398 (2012). But cf. Ralitsa Petkova & Lu Zhang, Is Value Riskier Than Growth?, 78 J. Fin. Econ. 187–202, 200 (2005) (concluding that a time-varying risk measure based on the difference between value betas and growth betas does point “in the right direction,” but ultimately “is far too small to explain the observed magnitude of the value premium within the conditional CAPM”).

  21. 21.

    Baltussen, Post & Van Vliet, supra note 20, at 3383.

  22. 22.

    See generally, e.g., Rajnish Mehra & Edward C. Prescott, The Equity Premium: A Puzzle, 15 J. Monetary Econ. 145–161 (1985); Rajnish Mehra & Edward C. Prescott, The Equity Premium Puzzle in Retrospect, in Handbook of the Economics of Finance 889–938 (George M. Constantinides, Milton Harris & René M. Stulz eds., 2003).

  23. 23.

    Rajnish Mehra & Edward C. Prescott, The Equity Premium: A Puzzle, 15 J. Monetary Econ. 145–161, 146 (1985). On pure exchange economies, see generally Robert E. Lucas, Jr., Asset Prices in an Exchange Economy, 46 Econometrica 1429–1445 (1978).

  24. 24.

    Mehra & Prescott, The Equity Premium, supra note 23, at 146.

  25. 25.

    See Roger G. Ibbotson & Peng Chen, Long-Run Stock Returns: Participating in the Real Economy, 59:1 Fin. Analysts J. 88–98 (Jan./Feb. 2003).

  26. 26.

    Rajnish Mehra, The Equity Premium: Why Is It a Puzzle?, 59:1 Fin. Analysts J. 54–69, 54 (Jan./Feb. 2003); Rajnish Mehra & Edward C. Prescott, The Equity Premium in Retrospect, in 1 Handbook of the Economics of Finance 888–936, 889 (George M. Constantinides, Milton Harris & René M. Stulz eds., 2003).

  27. 27.

    Mehra, supra note 26, at 60; Mehra & Prescott, The Equity Premium in Retrospect, supra note 26, at 909.

  28. 28.

    See Narayana R. Kocherlakota, The Equity Premium: It’s Still a Puzzle, 34 J. Econ. Lit. 42–71 (1996).

  29. 29.

    Mehra, supra note 26, at 60; Mehra & Prescott, The Equity Premium in Retrospect, supra note 26, at 909.

  30. 30.

    Estrada, Downside Risk and Capital Asset Pricing, Chap. 5 , supra note 42, at 183; Estrada, Systematic Risk in Emerging Markets, Chap. 5, supra note 36, at 375–376. The same passage appears in both articles; I have omitted Estrada’s footnote crediting Mark Kritzer for the observation regarding contagion.

  31. 31.

    See Kahneman, Sinking, Fast and Slow, Chap. 4, supra note 74, at 281.

  32. 32.

    See, e.g., Gary Charness, David Masclet & Marie Claire Villeval, The Dark Side of Competition for Status, 60 Mgmt. Sci. 38–55 (2014); Simon Dato & Petra Nieken, Gender Differences in Competition and Sabotage, 100 J. Econ. Behav. & Org. 64–80 (2014); Thomas Dohmen, Armin Falk, Klaus Flessbach, Uwe Sunde & Bernd Weber, Relative Versus Absolute Income, Joy of Winning, and Gender: Brain Imaging Evidence, 95 J. Pub. Econ. 279–285 (2011); Camellia M. Kuhnen & Agnieszka Tymula, Feedback, Self-Esteem, and Performance in Organizations, 58 Mgmt. Sci. 94–113 (2012); Mark Sheskin, Paul Bloom & Karen Wynn, Anti-Equality: Social Comparison in Young Children, 130 Cognition 152–156 (2014).

  33. 33.

    See Malcolm P. Baker & Jeffrey Wurgler, Comovement and Predictable Relations Between Bonds and the Cross-Section of Stocks, 2 Rev. Asset Pricing Stud. 5787 (2012).

  34. 34.

    Liebowitz, Bova & Hammond, Chap. 4, supra note 29, at 265.

  35. 35.

    See generally Geert Bekaert, Campbell R. Harvey & Angela Ng, Market Integration and Contagion, 78 J. Bus. 39–69 (2005).

  36. 36.

    Thomas J. Flavin & Ekaterini Panopoulou, Detecting Shift and Pure Contagion in East Asian Equity Markets: A Unified Approach, 15 Pac. Econ. Rev. 401–421, 401 (2010).

  37. 37.

    Id. See generally Toni Gravelle, Maral Kichian & James Morley, Detecting Shift-Contagion in Currency and Bond Markets, 68 J. Int’l Econ. 409–423 (2006).

  38. 38.

    Flavin & Panopoulou, supra note 36, at 401–402.

  39. 39.

    Id. at 402. See generally Marcello Pericoli & Massimo Sbracia, A Primer in Financial Contagion, 17 J. Econ. Surveys 571–608 (2003).

  40. 40.

    Flavin & Panopoulou, supra note 36, at 402.

  41. 41.

    See id.

  42. 42.

    See Brad M. Barber & Terrance Odean, All That Glitters: The Effect of Attention and News on the Buying Behavior of Individual and Institutional Investors, 21 Rev. Fin. Stud. 785–818 (2008).

  43. 43.

    John Maynard Keynes, A Treatise on Probability 23 (1921); accord Robert J. Shiller, Irrational Exuberance 253 (3d ed. 2015).

  44. 44.

    Shiller, supra note 43, at 253.

  45. 45.

    Liebowitz, Bova & Hammond, Chap. 4, supra note 29, at 265.

  46. 46.

    See Lasse Heje Pedersen, When Everyone Runs for the Exits, 5 Int’l J. Cent. Banking 177–179 (2009).

  47. 47.

    See Amos Tversky & Daniel Kahneman, Rational Choice and the Framing of Decisions, 59 J. Bus. S251–S278 (1986); Amos Tversky & Daniel Kahneman, The Framing of Decisions and the Psychology of Choice, 211 Science 453–481 (1981).

  48. 48.

    See Philippe Jorion, Mean/Variance Analysis of Currency Overlays, 50:3 Fin. Analysts J. 48–56, 52 (May/June 1994).

  49. 49.

    See generally Kahneman, Sinking, Fast and Slow, Chap. 4, supra note 74, at 19–105; supra § 4.4, at 47–49.

  50. 50.

    See sources cited, Chap. 5, supra note 46.

  51. 51.

    See Ang, Chen & Xing, Chap. 5, supra note 53, at 1227 (defining downside beta as \( {\beta}_{-}={\rho}_{-}\frac{\sigma_{a,-}}{\sigma_{m,-}} \).

  52. 52.

    Andrew Ang, Robert J. Hodrick, Yuhang Xing & Xiaoyan Zhang, The Cross-Section of Volatility and Expected Returns, 61 J. Fin. 259–299, 260 (2006). See generally John Y. Campbell & Ludger Hentschel, No News Is Good News: An Asymmetrical Model of Changing Volatility in Stock Returns, 31 J. Fin. Econ. 281–318 (1992); Kenneth R. French, G. William Schwert & Robert F. Stambaugh, Expected Stock Returns and Volatility, 19 J. Fin. Econ. 3–22 (1987).

  53. 53.

    See sources cited Chap. 5, supra note 46.

  54. 54.

    Ang, Chen & Xing, Chap. 5, supra note 53, at 1228.

  55. 55.

    For introductions to meiosis and ploidy, biological concepts that arise rarely, if at all, in the language or logic of finance, see Harris Bernstein & Carol Bernstein, Evolutionary Origin of Recombination During Meiosis, 60 BioScience 498–505 (2010); Laura Wegener Parfrey, Daniel J.G. Lahr & Laura A. Katz, The Dynamic Nature of Eukaryotic Genomes, 25 Molecular Biol. & Evol. 787–794 (2008); J.M. deWet, Origins of Polyploids, 13 Basic Life Scis. 3–15 (1979). In meiosis, a cell divides itself into two parts, each containing half of its chromosomes. Ploidy refers to the number of sets of chromosomes within a cell. A healthy haploid cell, usually a gamete (egg or sperm), contains a single copy of each chromosome. The typical somatic cell of a diploid species (such as humans) contains two complete haploid sets of chromosomes.

  56. 56.

    See Andrew Ang & Joseph Chen, Asymmetric Correlations of Equity Portfolios, 63 J. Fin. Econ. 443–494, 444 (2002); Longin & Solnik, Chap. 4, supra note 28, at 650–51.

  57. 57.

    See Liebowitz, Bova & Hammond, Chap. 4, supra note 29, at 263, 267–269 (identifying a value called “stress beta” that is equal to “the original beta multiplied by” a quantity equivalent to v – c – ); Ang & Chen, supra note 56, at 461 (identifying “the ratio of upside portfolio volatility to market volatility” and its downside counterpart); Harvey, Predictable Risk and Returns in Emerging Markets, supra note 5, at 809 (“The correlation is related to beta by the ratio of the world and country standard deviations.”).

  58. 58.

    Ang, Hodrick, Xing & Zhang, supra note 52, at 260.

  59. 59.

    See Robert C. Camp & Arthur A. Eubank, Jr., The Beta Quotient: A New Measure of Portfolio Risk, 7:4 J. Portfolio Mgmt. 53–58 (Summer 1981).

  60. 60.

    Id. at 54. In terms of correlation, an r 2 value of 0.85 corresponds to ρ ≈ 0.922.

  61. 61.

    Chris Tofallis, Investment Volatility: A Critique of Standard Beta Estimation and a Simple Way Forward, 187 Eur. J. Oper. Research 1358–1367, 1361 (2008).

  62. 62.

    Id. at 1363.

  63. 63.

    Id. at 1361; see also id. at 1363.

  64. 64.

    Cf. Camp & Eubank, supra note 59, at 54 (conceding that “the use of beta to measure [the] risk” of a “well-diversified” portfolio “is appropriate and adequate”).

  65. 65.

    Id. at 56.

  66. 66.

    Tofallis, supra note 61, at 1361.

  67. 67.

    See generally Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Asset 183–206 (3d ed. 2012).

  68. 68.

    See, e.g., Peter Butler & Keith Pinkerton, Company Specific Risk—A Different Paradigm: A New Benchmark, 25:1 Bus. Valuation Rev. 22–28 (Spring 2006); Peter Butler & Keith Pinkerton, There Is a New “Beta” in Town, and It’s Not Called Total Beta for Nothing!, 15:3 Bus. Valuation Update 7–10 (March 2009).

  69. 69.

    Camp & Eubank, supra note 59, at 56.

  70. 70.

    Compare, e.g., Larry J. Kasper, Fallacies of the Butler-Pinkerton Model and the Diversification Argument, Value Examiner, Jan.-Feb. 2010, at 8–20 with Tony van Zijk, Beta Loss, Beta Quotient: Comment, 11:4 J. Portfolio Mgmt. 75–78 (Summer 1985).

  71. 71.

    See generally Tuomo Vuolteenaho, What Drives Firm-Level Stock Returns?, 57 J. Fin. 233–264 (2002).

  72. 72.

    See Fangjian Fu, Idiosyncratic Risk and the Cross-Section of Expected Stock Returns, 91 J. Fin. Econ. 24–37 (2012).

  73. 73.

    See John Y. Campbell, Martin Lettau, Burton G. Malkiel & Yexiao Xu, Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk, 56 J. Fin. 1–43 (2001).

  74. 74.

    Morelli, supra note 14, at 267. See generally K.C. Chan & Nai-Fu Chen, Structural and Return Characteristics of Small and Large Firms, 46 J. Fin. 1467–1484 (1991).

  75. 75.

    See Malcolm Baker, Brendan Bradley & Jeffrey Wurgler, Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly, 67:1 Fin. Analysts J. 40, 46 (Jan./Feb. 2011).

  76. 76.

    Ang, Chen & Xing, Chap. 5, supra note 53, at 1193.

  77. 77.

    Baker, Bradley & Wurgler, supra note 75, at 40.

  78. 78.

    Id. (emphasis in original).

  79. 79.

    Robert A. Haugen & A. James Heins, Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles, 10 J. Fin. & Quant. Analysis 775–784, 782 (1975) (emphasis added).

  80. 80.

    Ang, Hodrick, Xing & Zhang, supra note 52, at 296; accord Baker, Bradley & Wurgler, supra note 75, at 43; see also Andrew Ang, Robert J. Hodrick, Yuhang Xing & Xiaoyan Zhang, High Idiosyncratic Volatility and Low Returns: International and Further U.S. Evidence, 91 J. Fin. Econ. 1–23 (2009).

  81. 81.

    See, e.g., David C. Blitz & Pim van Vliet, The Volatility Effect: Lower Risk Without Lower Return, 34:1 J. Portfolio Mgmt. 102–113 (Fall 2007); Roger Clarke, Harindra de Silva & Steven Thorley, Minimum-Variance Portfolios in the U.S. Equity Market, 33:1 J. Portfolio Mgmt. 10–24 (Fall 2006); Andrea Frazzini & Lasse Heje Pedersen, Betting Against Beta, 111 J. Fin. Econ. 1–25 (2014); Robert A. Haugen & Nardin L. Baker, The Efficient Market Inefficiency of Capitalization-Weighted Stock Portfolios, 17:3 J. Portfolio Mgmt. 35–40 (Spring 1991); cf. Javier Estrada & Ana Paula Serra, Risk and Return in Emerging Markets: Family Matters, 15 J. Multinat’l Fin. Mgmt. 257–272, 267 (2004) (finding, “counterintuitively,” that “low-risk portfolios” in emerging markets “outperform … high-risk portfolios over 20 years,” at least “when portfolios are rebalanced every 10 years”).

  82. 82.

    Baker, Bradley & Wurgler, supra note 75, at 43.

  83. 83.

    Ang, Hodrick, Xing & Zhang, supra note 52, at 297.

  84. 84.

    Id. at 260 (emphasis added); see also id. (“If the price of aggregate volatility is negative, stocks with large, positive sensitivity should have low average returns.”).

  85. 85.

    Baker, Bradley & Wurgler, supra note 75, at 43; see also Jonathan Fletcher, On the Conditional Relationship Between Beta and Return in International Stock Returns, 9 Int’l Rev. Fin. Analysis 235–245, 240 (2000).

  86. 86.

    Edward H. Bowman, A Risk/Return Paradox for Strategic Management, 21 Sloan Mgmt Rev. 17–33 (1980).

  87. 87.

    See Edward H. Bowman, Risk Seeking by Troubled Firms, 23 Sloan Mgmt. Rev. 33–42 (1982); Edward H. Bowman, Content Analysis of Annual Reports for Corporate Strategy and Risk, 14 Interfaces 61–71 (1984).

  88. 88.

    Manuel Núñez Nickel & Manuel Cano Rodriguez, A Review of Research on the Negative Accounting Relationship Between Risk and Return: Bowman’s Paradox, 30 Omega 1–18, 1 (2002). Omega describes itself as “The International Journal of Management Science.”

  89. 89.

    Id. at 2.

  90. 90.

    Id.

  91. 91.

    See Fama & French, The Cross-Section of Stock Returns, Chap. 4, supra note 4; Nickel & Rodriguez, supra note 88, at 1.

  92. 92.

    Nickel & Rodriguez, supra note 88, at 2. Compare sources cited, Chap. 4, supra note 49 (casting beta aside in favor of Fama and French’s value and small-size factors) with sources cited, Chap. 4, supra note 65 (attempting to rehabilitate beta by declaring this measure’s purported death to be premature).

  93. 93.

    Philip Bromiley, Kent D. Miller & Devaki Rau, Risk in Strategic Management Research, in The Blackwell Handbook of Strategic Management 259–298, 259 (Michael A. Hitt., R. Wedward Freeman & Jeffrey S. Harrison eds., 2006).

  94. 94.

    Id.

  95. 95.

    Id.

  96. 96.

    Nickel & Rodriguez, supra note 88, at 2; see also Gerry McNamara & Philip Bromiley, Risk and Return in Organizational Decision Making, 42 Acad. Mgmt. J. 330–339, 330 (1999).

  97. 97.

    See, e.g., Sayan Chatterjee, Michael H. Lubatkin & William S. Schulze, Toward a Strategic Theory of Risk Premium: Moving Beyond CAPM, 24 Acad. Mgmt. Rev. 556–567 (1999); Avi Fiegenbaum & Howard Thomas, Dynamic and Risk Management Perspectives on Bowman’s Risk-Return Paradox for Strategic Management: An Empirical Study, 7 Strat. Mgmt. J. 394–407 (1986); Rajaram Veliyath & Stephen P. Ferris, Agency Influences on Risk Reduction and Operating Performance: An Empirical Investigation Among Strategic Groups, 39 J. Bus. Research 219–230 (1997).

  98. 98.

    See Moon K. Kim & Badr E. Ismail, An Accounting Analysis of the Risk-Return Relationship in Bull and Bear Markets, 7 Rev. Fin. Econ. 173–182 (1998).

  99. 99.

    See Torben J. Andersen, Jerker Denrell & Richard A. Bettis, Strategic Responsiveness and Bowman’s Risk-Return Paradox, 28 Strat. Mgmt. J. 407–429 (2007); Joachim Henkel, The Risk-Return Paradox for Strategic Management: Disentangling True and Spurious Effects, 30 Strat. Mgmt. J. 287–303 (2009).

  100. 100.

    See, e.g., Avi Fiegenbaum, Prospect Theory and the Risk-Return Association: An Empirical Examination in 85 Industries, 14 J. Econ. Behav. & Org. 187–203 (1990); Avi Fiegenbaum & Howard Thomas, Attitudes Toward Risk and the Risk-Return Paradox: Prospect Theory Explanations, 31 Acad. Mgmt. J. 85–106. See generally Nickel & Rodriguez, supra note 88, at 4–5.

  101. 101.

    See sources cited, Chap. 4, supra note 49.

  102. 102.

    See Chong & Phillips, Chap. 6, supra note 2, at 351 (acknowledging that the connections between single-sided beta and the Fama–French three-factor model remain largely unexplored).

  103. 103.

    See Xi Li, Rodney N. Sullivan & Luis García-Feijóo, The Limits to Arbitrage and the Low-Volatility Anomaly, 70:1 Fin. Analysts J. 52–63, 53, 62 (Jan./Feb. 2014).

  104. 104.

    Mark Grinblatt & Sheridan Titman, Financial Markets and Corporate Strategy 392 (2d ed. 2001).

  105. 105.

    Lu Zhang, The Value Premium, 60 J. Fin. 67–103, 67 (2005) (describing the tendency of “value stocks [to] earn higher expected returns than growth stocks” as “a troublesome anomaly for rational expectations”).

  106. 106.

    See sources cited, Chap. 4, supra note 51.

  107. 107.

    See generally Nai-Fu Chen, Richard Roll & Stephen A. Ross, Economic Forces and the Stock Market, 59 J. Bus. 383–403, 386–388 (1986) (identifying the growth rate of industrial production as a risk factor that is priced by the stock market).

  108. 108.

    See Laura Xiaolei Liu & Lu Zhang, Momentum Profits, Factor Pricing, and Macroeconomic Risk, 21 Rev. Fin. Stud. 2417–2448, 2437 (2008). But see John M. Griffin, Xiuqing Ji & J. Spencer Martin, Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole, 58 J. Fin. 2515–2547, 2515 (2003) (finding no “evidence that macroeconomic risk variables can explain momentum” and concluding instead that “momentum profits around the world are large and statistically reliable in both good and bad economic states”).

  109. 109.

    See Clifford S. Asness, Tobias J. Moskowitz & Lasse Heje Pedersen, Value and Momentum Everywhere, 68 J. Fin. 929–985, 930, 962 (2013).

  110. 110.

    Alles & Murray, supra note 5, at 2508 (finding “no evidence” that Fama and French’s factors fully capture—and therefore wholly supersede—downside risk concerns embodied in single-sided measures of volatility and correlation).

  111. 111.

    Estrada & Serra, supra note 81, at 259 (emphases in original).

  112. 112.

    See generally Victor Ricciardi, Risk: Traditional Finance Versus Behavioral Finance, in 3 Handbook of Financial Valuation, Financial Modeling, and Quantitative Tools 11–38 (Frank J. Fabozzi ed., 2008).

  113. 113.

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    Id.

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    Id.

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    See Estrada, Downside Risk and Capital Asset Pricing, Chap. 5, supra note 42, at 175–176 (exhibit 1).

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    Id.

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    Id. at 669–670.

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    Id.

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    See Ang, Chen & Xing, Chap. 5, supra note 53, at 1199.

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    Id.

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    Id.

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Chen, J.M. (2016). Sinking, Fast and Slow: Relative Volatility Versus Correlation Tightening. In: Postmodern Portfolio Theory. Quantitative Perspectives on Behavioral Economics and Finance. Palgrave Macmillan, New York. https://doi.org/10.1057/978-1-137-54464-3_7

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